Temperature scanning reaction method

ABSTRACT

A method for rapidly collecting kinetic rate data from a temperature scanning reactor for chemical reactions. The method, which is particularly useful for studying catalytic reactions, involves ramping (scanning) of the input temperature to a reactor and recording of output conversion and bed temperature without waiting for isothermal steady state to be established.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of our earlier filed U.S.patent application Ser. No. 07/833,182 filed Feb. 10, 1992, nowabandoned.

FIELD OF THE INVENTION

This invention relates to a method and apparatus for determining ratesof reaction in a chemical reactor system.

BACKGROUND OF THE INVENTION

The acquisition of kinetic data from a chemical reaction system isusually a laborious, time consuming and expensive undertaking. As aconsequence, evaluation of catalysts and reaction conditions, in thechemical industry, for example, is often carried out with scanty datawhich does not allow for a full understanding of the system under study.Conventional methods generally include collecting iso-thermal conversiondata at steady state for a number of feed rates. Because of operatingrequirements, such as waiting for steady state, start-up, shutdown etc.,it is usually only possible to make 1-5 runs per day in any givensystem. At least 30 runs are needed over a range of 3 or 4 temperatures.About 8-10 space velocities are required at each temperature, and henceit will be seen that such a study will take about two months tocomplete. This time period may be considerably increased if repeat runsare required to verify catalyst stability over this length of time or toobtain a statistical measure of variance or if feed composition ofreactant concentration are to be varied. Frequently, therefore, theremay be as much as one person-year required for a full research study.There is, therefore, a considerable need for an improved method ofacquiring kinetic rate data for chemical reactors.

OBJECT OF INVENTION

An object of the present invention is to provide a method fordetermining kinetic rate data for chemical reactors which is at least anorder of magnitude faster than conventional methods.

BRIEF STATEMENT OF INVENTION

Thus, by one aspect of this invention there is provided a method forrapid collection of kinetic rate data from a temperature scanningreactor in which a feed stock is reacted under non-steady stateconditions to form a conversion product comprising,

ramping the input temperature of said feed stock rapidly over a selectedrange of temperature,

continuously monitoring output conversion and output temperature whileramping the input temperature and determining a rate of reactionrepresentative of steady state conditions from input and outputtemperature and output conversion data obtained during said non-steadystate operation of the reactor.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a graph showing constant rate curves of methanol formation;

FIG. 2 is a graph showing methanol conversion versus rate⁻¹ ;

FIG. 3 is a graph showing methanol conversion versus input temperatureT_(i) at three constant space velocities or space times; WHSV=0.1(τ=10); WHSV=1.1 (τ=0.91) and WHSV=2.1 (τ=0.48);

FIG. 4 is a graph showing methanol conversion versus output temperatureT_(o) at the same space velocities as in FIG. 3.

FIG. 5 are conversion curves X_(A) versus output temperature T_(o) atconstant space time τ but varying input temperatures T_(i) superimposedon the equilibrium curve for the system;

FIG. 6 is a graph showing methanol conversion versus rate constant inputtemperatures T_(i)

    T.sub.1 =536.7° K.,T.sub.2 =570.7° K. and T.sub.3 =581.3° K.;

FIG. 7 is a graph of stimulated behavior of output temperature T_(o) asa function of input temperature in an adiabatic reactor for methanolsynthesis operating under the conditions of FIG. 1 at space velocitiesof FIG. 3;

FIG. 8 is a graph of methanol conversion versus temperature for theinitial temperatures T₁ =536.7° K., T₂ =570.7° K. determined in FIG. 3;and FIG. 9 is a schematic diagram of a temperature scanning reactor usedin the present invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENTS

FIG. 1 shows an equilibrium curve for methanol synthesis at 333atmospheres, two constant rate curves, and an adiabatic operating line,on coordinates showing the fraction converted versus the reaction-systemtemperature. Curve (A) corresponds to a rate of 10⁻⁸ kmol (kg cat)⁻¹ h⁻¹and in essence represents the equilibrium for this system. Curve Bcorresponds to a rate of 2×10⁻³ kmol (kg cat)⁻¹ h⁻¹, and, curve Ccorresponds to a rate of to 5×10⁻³ kmol (kg cat)⁻¹ h⁻¹. The feedcomposition has CO:H₂ :N₂ :He:CO₂ in the ratio 1:5:1:2:1 at 333atmospheres. The curves here and in the other figures were obtainedusing RESIM, an adiabatic reactor simulation program for the PC whichuses the kinetics and parameters quoted by Capelli et al in"Mathematical Model for Simulating Behavior of Fauser-MontecatiniIndustrial Reactors for Methanol Synthesis", I. & EC. Proc. Des. Dev.II(2), (1972) p. 184-190. These data were obtained using establishedkinetics. An adiabatic reactor whose feed enters at the temperaturewhere the operating line crosses X_(A) =0 will yield an output at steadystate which will invariably fall on this operating line. Exactly how farup this line the output will fall depends on the space velocity used. Inthe ideal case, all features of FIG. 1 are fixed for each pressure,catalyst, and feed composition including changes in inerts.

The equation of the operating line in this simplest case is:

    X.sub.A =C.sub.p T/-H.sub.r                                (1)

Thus, X_(A) is directly proportional to T. This is true in systems whichdo not have significant secondary reactions or parallel reactions ofdifferent orders and do not lose heat to the reactor components or thesurroundings. The matter becomes somewhat more complicated in the realworld when the reactor and catalyst have finite heat capacities and heatloss may be unavoidable. In that case, the basic heat balance equationbecomes: ##EQU1## Because a scanning reactor will be examined, whichoperates in a transient or non-steady state mode, the accumulation termcannot be ignored. By convention, the input condition is the enthalpydatum: i.e. heat input=0.

The heat output term will depend on the composition of the products andcan be written:

    heat output=C.sub.p (T.sub.o -Thd i)(1-X.sub.A)+C.sub.pp1 (T.sub.o -T.sub.i)(X.sub.A -X.sub.p)(X.sub.A -X.sub.p)+C.sub.pp2 (T.sub.o -T.sub.i X.sub.p)

where only one primary product p1 and one secondary product p2 arepostulated. More complex systems can be envisioned without changing theoverall conclusions.

In accounting for heats of reaction, the heat of conversion of reactantto primary product p1 and the heat of conversion of that product to thesecondary product p2 must be considered:

    heat generation by reaction=H.sub.ri X.sub.A +H.sub.pi X.sub.p

where X_(p) is the fraction of conversion of the reactant A to secondaryproducts p2 while X_(A) is the total fraction of reactant A converted.The subscripts ri and pi refer to heats of reaction of the feed A to p1and p2 at the inlet temperature T_(i).

In considering the accumulation terms, the heat capacity and mass ofeach of the components of the reactor must be considered. These willinclude walls, the catalyst charge and any other items present in thereactor: ##EQU2## where the term T_(s) is the temperature differencebetween the reactor walls etc. and the reactants and the subscript sindicates the component of the reactor. The heat capacity C_(ps) isexpressed in units commensurate with those of m, the quantity of a solidcomponent in the reactor. Since at the beginning of a temperature scanthe reactor is all at T_(i), T_(s) is a function of both time andposition in the reactor.

Finally, heat losses from the reactor will take the form: ##EQU3## whereh is the heat transfer coefficient, s is the heat transfer surface andT_(f) is the driving force due to temperature difference between thereactor component f and its surroundings. Again, T_(f) will be afunction of time. These terms are collected to present a more completeform of equation 1 ##EQU4## It can be seen that Equation 1a reduces toEquation 1 when all of the following are true:

a) secondary reaction does not occur and X_(p) =0

b) the heat capacity of the reactor is very small and C_(ps) →0 or whenheat transfer to the reactor material is very slow, or at steady statewhen T_(s) =0

c) heat loss from the reactor components is small because

1) h_(f) are all very small

2) T_(f) is minimized by appropriate instrument design.

Under appropriate conditions, there will exist a unique operating linefor every real reactor under a prescribed set of operating conditionsand, in the case of the adiabatic reactor, it is obvious that theoperating line is unique. The reaction rate curves, on the other hand,are independent of the heat effects and will depend only on temperature,feed composition, catalyst activity and pressure regardless ofadiabaticity.

To get from the input condition shown as T₁ in FIG. 1 to an outputcondition at B₁ using a plug flow reactor (PFR) will require a certainspace time τ_(B1). To reach condition C₁ from T₁ will require adifferent space time .sup.τ C₁ >.sup.τ B₁, etc. In a PFR, each point onthe operating line is reached at a unique space time.

At the space velocity which results in .sup.τ B₁, an output conversionX_(AB1) will be achieved which will be changing at a rate correspondingto constant rate curve B, regardless of how this point is reached,either along an ideal operating line given by equation 1 or along a morecomplicated path given by equation 1a or its elaborations. If spacevelocity is decreased, i.e. increase τ to .sup.τ C₁, condition C₁ willbe reached which is the maximum rate achievable on the operating linestarting at T₁ and lies on constant rate curve C. Further increases in τwill result in higher conversions but at decreasing rates. On the way toequilibrium conversion on Curve A, curve B will be encountered again atcondition B₂. The rate at B₁ and B₂ will be the same; at B₁ it willoccur at low conversion and low temperature while at B₂ it will takeplace at high conversion and high temperature. It is clear therefore,that the reactor can be operating at B₁ or B₂ under steady or non-steadystate conditions, and it is apparent that the temperature profile alongthe length of the reactor, before the condition at B₁ or B₂ is reached,need not be the same as that which would result if input temperature wasconstant. It will be appreciated that, in contrast, a steady statecondition is one which would eventually be reached at a sufficientlylong time from the beginning of the observation if the inputtemperature, composition etc. is maintained at a constant value. If thisconstant value is changed, a finite amount of time must elapse before anew steady state is achieved. Nevertheless, at each instant during thetransient the instantaneous rate of reaction of a system at point B₁ orB₂ is defined by the temperature and conversion alone. That condition iscompletely independent of the conditions along the reactor preceding orsucceeding that condition and hence is independent of whether the systemas a whole is at steady state or not.

FIG. 2 shows a plot of the reciprocal rate versus conversion. Fromreactor design, theory, this information is used to size the reactorusing the general equation: ##EQU5##

The area under the curve on FIG. 2 between X_(A) =0 and X_(A) =X_(Af) is##EQU6## Equation 3 is valid whether the temperature of the system isconstant or not. At constant temperature T:

    dX.sub.A /-r.sub.A |.sbsb.T=dr/C.sub.AO |.sbsb.T(4)

or rearranging

    C.sub.AO dX.sub.A /dτ|.sbsb.T=-r.sub.A |.sbsb.T(5)

In order to obtain the rate at a given reaction temperature;, the valueof dX_(A) /d τ at that temperature is required. This information isroutinely obtained in isothermal reactors by incrementing space velocityin successive runs, however, in TS-PFRs, it may be most readilyobtained, not by the procedure of incrementing the input space velocity,but by the simple procedure of ramping the input temperature at constantspace velocity and composition, so as to scan an input temperature rangefrom T_(min) to T_(max) and observing the conversion X_(A) andtemperature T_(o) at the outlet of the reactor at each instant duringthe scan.

The temperature scanning procedure is equivalent to investigating theoutput condition, at constant τ, on a succession of operating lines, asidentified for the 2.1 WHSV curve on FIGS. 3 and 8 by points 3, 4, and5. In FIG. 3a series of curves showing how X_(A) varies with the inputtemperature (T_(i)) as a result of scans for various constant values ofτ, all at constant composition and pressure are shown. In practise, theinput temperature is ramped until a preset maximum output temperatureT_(omax) is recorded, to protect the reactor or the catalyst or simplyto avoid reaching equilibrium conversion. After each scan, a data setconsisting of triplets of readings of T_(i), T_(o) and X_(A) atcorresponding times during the scan is collected.

Such a data set was used to produce FIG. 3 and can also be plotted inanother form by plotting X_(A) versus T_(o) as shown in FIG. 4. There islittle point in pushing the inlet temperature too high as can be seen bysuperimposing FIG. 4 on the rate curves of FIG. 1 as shown in FIG. 5. Atinput temperatures above a certain value, the equilibrium condition atthe output, as indicated by the uppermost curve corresponding toWHSV=0.1 is obtained. To investigate the kinetics of a reaction it ispreferable to stay below, in fact well away from equilibriums.

In FIG. 3, it can be seen that at any T_(i) values of X_(A) at as manyvalues of r as have been investigated can be obtained. In fact, manysets of such values at various inlet temperatures T_(i), within therange of temperature studied can be obtained. Each such set can then beplotted as shown in FIG. 6. The curves on FIG. 6 are curves ofconversion vs space time along operating lines starting at the varioustemperatures indicated. Differentiating the curves on FIG. 6 producesdX_(A) /dτ at constant T_(i) and the information necessary to plot FIG.2. These are the rates which might be observed along an operating linestarting at a given T_(i) if such a measurement were possible. Thefunctional form of the operating line does not matter, as long as thereexists a unique operating line for the conditions used.

From a family of curves such as those shown on FIG. 2, the constant ratecurves shown on FIG. 1 can be constructed and hence all the informationnecessary for kinetic model fitting can be obtained. Experimentaloperating lines which can be used to evaluate the heat effects involvedin the reaction can also be generated. For each X_(A) and T_(i) fromFIG. 3, at T_(o) can be read off, for the same r, on FIG. 4. These givea set of values of X_(A) and T_(o) at constant T_(i). This data, whenplotted as X_(A) vs T_(o), will produce an experimental operating line.

If the experimental operating lines are almost straight, it can beassumed that the reaction products either are stable or do not have asignificant heat of reaction during conversion to secondary products andthat the heat loss and accumulation terms in equation 1a areunimportant. If the primary products react to secondary productsendothermally, the operating lines will be concave or tend to curl up.Large temperature effects in the heat capacities of products andreactants can also induce curvature in the operating lines. Othereffects, such as heat transfer from the reactants to the catalyst orother materials in the reactor, will also induce a concave curvature ofthe operating lines in ways which in some cases can be quantified.Careful determination of reactor and catalyst heat capacities, of theheats of reaction for secondary reactions and minimization of heat lossin order to approach adiabatic conditions, can be used to derive afuller description of the observed operating lines. The time-dependentterms of Equation la can also be evaluated by suitable instrumentcalibration procedures.

Even if nothing of the chemistry, thermodynamics or kinetics of thereaction is known, useful qualitative information about the reactionfrom data such as that shown in FIG. 3 can be obtained. A TemperatureScanning Reactor (TSR) run plotted on the coordinates of FIG. 3, whenrepeated on a different catalyst formulation, will show if the newcatalyst is more active. The curves for the more active catalyst wouldlie above those for the less active. There is nothing to prevent twosuch curves, obtained on different catalysts, from crossing. This wouldsimply indicate that the activation energies or mechanisms of reactionare different on the two catalysts, thereby providing additional usefulinformation.

Experimental Procedure

An automated temperature scanning reactor 1 apparatus, as seen in FIG.9, can be set up in such a way that feed space velocity is maintained ata constant value, while reactant input temperature T_(i) at gas inlet 2is ramped over a range of temperatures ending at some input temperaturewhich results in a maximum allowed output temperature T_(omax) at gasoutlet 3. The reactor 1 is then cooled, equilibrated at its initialinput temperature T_(imin) and a new space velocity selected. Theramping of the temperature is repeated and stopped again when T_(omax)is reached. The procedure is repeated at as many space velocities asnecessary, say about 10. The data gathered during each temperature scanconsist of a set of T_(i) and corresponding T_(o). If necessary, X_(A)is followed at the same time using on-line FTIR or MS analysis using amass spectrometer 4 or other analytical facility for continuousmonitoring of output conversion. In the best of cases, X_(A) may berelated to T by calculation or by auxiliary experiments.

An experimental setup which approaches an ideal adiabatic reactor isuseful for simplifying the measurement of X_(A). In the ideal case,equation 1 will apply and X_(A) can be calculated from the differencebetween T_(o) and T_(i). Departures from the adiabatic condition maynecessitate the evaluation of the correction terms in equation la. Ifthe necessary terms can be quantified, an instantaneous conversionmonitoring detector at the outlet of the reactor is unnecessary. Thus aseries of temperature scans will yield for each space velocity T a setof data consisting of the triplets T_(i), T_(o) and X_(A).

The data logging, temperature scanning and space velocity changes canall be put under the control of a computer 5. The experimental dataconsisting of sets of T_(i) and T_(o) and X_(A) at various will belogged numerically or presented graphically on recorder 6 to look likethe curves shown in FIG. 3, 4 or 7. These are the raw datapresentations.

Using X_(A) data in the form shown in FIG. 4, one or more outputtemperatures, at which isothermal rate constants are required areselected. In this example T=640K is selected and it is found that theoutput conversions which occur at this temperature at the three spacevelocities of 0.1, 1.1 and 2.1 hr⁻¹ are 0.39, 0.27 and 0.23. Thecorresponding conditions are labeled with circled 1, 2 and 3 for crossreference with other figures. These conversions are used in FIG. 3 tofind the input temperatures T_(i) which lead to these output conditions.

Now, the values for T_(i) thus determined lie at X_(A) =0 on theoperating lines shown on FIG. 8 and X_(A) values form the FIG. 4 shouldall occur at 640K on the appropriate operating lines, as they clearlydo.

If enough scans at various values of τ are made it is possible to drawcurves such as those shown in FIG. 6 to an arbitrary degree of precisionby plotting X_(A) vs τ at each T_(i). FIG. 6 is simply a newrepresentation of the experimental data obtained by remapping the rawdata. Differentiating the curves on FIG. 6 produces values for plottingFIG. 2. FIG. 2 is also derived from the experimental data and representsthe rates of reaction along operating lines. Because it is necessary todifferentiate the data on FIG. 6 to obtain FIG. 2, it is clear thatenough runs with appropriate values of to make the numericaldifferentiation accurate will be required.

All that remains is to read the rates from the appropriate curves onFIG. 2 or from a plot of X_(A) vs rate for the X_(A) values at the 640Kselected on FIG. 4. This produces a set of rates and correspondingconversions at the selected reaction temperature T=640K. This isothermalrate data can be treated in a conventional fashion by fitting it topostulated kinetic models using graphical or statistical methods.

If the feed contains more than one component, this procedure should berepeated at a number of feed compositions in order to determine thekinetic effect of each component in the system. This can be automatedand need not complicate data gathering or interpretation beyond what isdescribed above.

Data Handling Formalism

All of the above can be readily programmed on a computer by applying thefollowing transformations of the basic T_(i), T_(o) and X_(A) data set.

Let

T_(i) (i) be the set of input temperatures with i=1 to m

τ(j) be the set of space times (or 1/WHSV) with j=1 to n

T_(o) (i,j) be the set of output temperatures

X_(A) (i,j) be the set of output conversions.

In practice the set of input and output temperatures will be dense, andlinear interpolations between adjacent measured results in the idirection can be applied. The space velocity set will, for reasons ofeconomy of effort, be much sparser and necessitate second orderinterpolations.

When the rate of reaction is considered, and if the data in the jdirection are sparse, a quadratic interpolation might be used: ##EQU7##for all j=2, . . . , n-1 while for the end members of the set ##EQU8##In the above, C_(AO) is the initial feed concentration of the basecomponent A whose conversion we are tracking. The formulas can besimplified somewhat by carrying out the experimental program so that forall j the step size in space time is the same:

    τ.sub.j -τ.sub.j-1 =constant                       (10)

Alternately spline functions may be fitted and differentiated directly.

A complete table of rates τ(i,j) can therefore be assembled inone-to-one correspondence with the measurements of T_(o) and X_(A). Thiscan then be used in a program which simultaneously evaluates all rateconstants and their Arrhenius parameters.

If the density in the i direction is high, rates at any desiredtemperature can be interpolated within the range of the scan by linearinterpolation and rate constants at selected isothermal conditions canbe evaluated. In the linear case, an output temperature T_(o) (k,j) suchthat k is constant for all j is selected. Output temperatures whichbracket the desired T_(o) at each r are identified. Let these outputtemperatures be:

    lower value=T.sub.o (1,j)

    higher value=T.sub.o (h,j)

where 1 and h correspond to actually measured values of T_(o) atconditions 1 and h. Each of these conditions has a corresponding rater(1,j) and r(h,j). These can be linearly interpolated to give the newrates at k enlarging the set of available temperature conditions to m+1:##EQU9## The corresponding conversion is: ##EQU10## In this way, a setof r(k,j) and corresponding X_(A) (k,j) values is calculated. Such setsof isothermal rates and corresponding conversions can be obtained atmany temperatures. They can be processed further by well-known means todetermine the best kinetic expression and its parameters using modeldiscrimination techniques or, in cases when the rate expression isknown, to produce rate parameters, activation energies, etc. As FIG. 6makes plain, the important experimental requirement is that enough spacevelocities must be used to define the curves of X_(A) versus r insufficient detail so that equations 8-10, or other fitting procedures,are applicable within tolerable limits. The policy of keeping (τ_(j)-τ_(j-1)) constant, though it simplifies computation, may require alarge number of experiments to determine each X_(A) versus r curve withadequate precision. In general, it may be best to vary (τ_(j) -τ_(j-1))in order to minimize experimental effort and define each curve in asmuch detail as is necessary.

If each value of r can be scanned in 30 minutes, and if 10 values of τwill suffice for a given investigation, and if it takes 30 minutes toreset T_(i) min and change the space velocity, then a typical completelyautomated kinetic investigation using the TSAR should produce a best-fitmodel and its full set of kinetic parameters in something like a 24-hourperiod of automated data collection.

The data will yield, in principle, an unlimited number of isothermaldata sets of rate r_(A) and conversion X_(A) between the limits of thescans with something in the order of 10 space velocities at eachtemperature. This abundance of information, available in 24 hours,should be compared to the small set of data normally generated inmonths-long kinetic investigations.

It will be appreciated that while this invention has been described withreference to a plug flow reactor (PFR) and particularly an adiabaticplug flow reactor (APFR), the principles thereof are equally applicableto Continuous Stirred Tank Reactors (CSTR) and Batch Reactors.

The operating procedures for the CSTR are the same as for the Plug FlowReactor i.e. ramping input temperature and recording output temperatureand conversion. The equations required to calculate rates from CSTR dataare simpler than those described above for the PFR and this alone maymake the use of a suitable CSTR preferred in the application of theexperimental methods described above. The CSTR has other attractivefeatures such as better temperature control and lack of thermalgradients which may make its application even more attractive.

In the case of Batch Reactors it is possible to maintain uniformtemperature in the reactor while ramping the temperature over a selectedrange. The advantage of this type of reactor is that high pressurereactions or the reactions of solids may be investigated by ramping thetemperature of reactor contents while observing the degree of conversionand the temperature of the contents. This operation is advantageous incases where kinetics are at present being studied in batch autoclaves orin atmospheric pressure batch reactors.

The rate of data acquisition can be doubled over and above thatavailable by means of the procedures described above by the simpleexpedient of ramping the temperature up to a selected limit at a fixedspace velocity and, instead of cooling back to the initial conditionbefore the next data acquisition run, proceeding to change the spacevelocity at the high temperature limit and cooling the reactor with feedbeing supplied at the new space velocity. Data can then be acquired bothon the temperature up-ramp and on the down-ramp. The space velocity isonce again changed at the bottom of the ramp and a new up-rampinitiated. In this procedure there is essentially no "idle time" for thereactor and productivity of the apparatus is maximized.

Note also that the methods outlined in the above are applicable withminor alterations to cases where the reactor is not operated in anadiabatic manner, cases where the volume of the reacting mixture changesdue to conversion and a number of other complications which are known tooccur in such systems.

We claim:
 1. A method for rapid collection of kinetic rate data from atemperature scanning reactor in which a feed stock is reacted under nonsteady state conditions to form a conversion product comprising,rampingthe input temperature of said feed stock rapidly over a selected rangeof temperature, continuously monitoring output conversion and outputtemperature while ramping the input temperature and determining a rateof reaction which is representative of steady-state conditions frominput and output temperature and output conversion data obtained duringsaid non-steady state operation of the reactor.
 2. A method as claimedin claim 1 wherein said reactor is selected from the group consisting ofa plug flow, continuous stirred tank, and batch reactors.
 3. A method asclaimed in claim 2 wherein said reactor is operated in a non-adiabaticmode.
 4. A method as claimed in claim 2 wherein said reactor is operatedin an adiabatic mode.